1. Field of the Invention
The present invention relates generally to loop filters, and more particularly, to an apparatus for updating a gain of a loop filter with simple low-cost hard-ware components and without monitoring external noise.
2. Description of the Related Art
A timing recovery apparatus detects a timing error to recover a timing signal. FIG. 1 is a block diagram of a conventional timing recovery apparatus 100. Referring to FIG. 1, the timing recovery apparatus 100 includes a timing error detector 120, a loop filter 200, a numerically controlled oscillator (NCO) 140, and a timing error compensator 110.
The timing error detector 120 detects a timing error from a timing signal TS to generate a detected timing error signal TE. The loop filter 200 integrates the timing error signal TE to generate a loop filter output signal LF_out. The loop filter output signal LF_out is sent to the timing error compensator 110 via the NCO 140. The timing error compensator 110 compensates for the timing error TE to recover the timing signal TS. Such components 110, 120 140, and 200 of the timing recovery apparatus 100 are known to one of ordinary skill in the art.
Generally, the loop filter 200 is a kind of low pass filter that integrates the timing error signal TE to generate the loop filter output signal LF_out so as to determine the bandwidth of a feed-back loop formed by the components 110, 120 140, and 200. Thus, the loop filter 200 determines the sensitivity to noise and the stability of such a feed-back loop.
FIG. 2 is a block diagram of the loop filter 200 of FIG. 1. Referring to FIG. 2, the loop filter 200 is implemented as a PI (proportional-integral) controller and includes a phase error tracking unit 210, a frequency error tracking unit 220, and a summer 230. The phase error tracking unit 210 multiplies the timing error signal TE by a proportional gain KP to track a phase component of the timing error signal TE.
The frequency error tracking unit 220 accumulates prior values of the timing error signal TE multiplied by an integral gain KI, to track a frequency component of the timing error signal TE. The summer 230 adds the output signals of the phase error tracking unit 210 and the frequency error tracking unit 220 to generate the loop filter output signal LF_out that tracks both the phase component and the frequency component of the timing error signal TE.
The loop filter output signal LF_out is generated to be relatively large by setting the proportional and integral gains KP and KI to be relatively large initially such that the timing error compensator 110 rapidly converges to the timing signal TS. After a predetermined period of time, the timing signal TS has converged to a certain extent, and the proportional and integral gains KP and KI are decreased as the timing signal TS is recovered.
The proportional and integral gains KP and KI in the conventional loop filter 200 are estimated through modeling and simulation. However, such estimated gain values KP and KI may not reflect actual operating conditions of the loop filter 200 for factors not estimated in the modeling process. In that case, the timing signal TS cannot be properly recovered.
To solve such a problem, a Kalman algorithm is generally used to estimate the gain values of a loop filter. Generally, such a loop filter is referred to as a Kalman filter. The Kalman filter monitors noise caused by modeling or noise caused by a detector to estimate the gain. That is, the Kalman filter calculates an error covariance including external noise and calculates the gain of the Kalman filter from the error covariance. Thus, a variation in the external noise must be correctly monitored in order to obtain the correct gain of the Kalman filter. Such close monitoring of the external noise may be difficult to implement.
Furthermore, a Kalman algorithm includes many complicated calculating expressions. Accordingly, a Kalman filter performing complicated calculations, especially for dividing operations, has costly hardware. For example, U.S. Patent Application No. US 2004/0071207 uses interpolation residual calculation which includes dividing operations for an adaptive Kalman filter. Alternatively, U.S. Pat. No. 6,766,153 to Kozak et al. uses a Kalman gain coefficient table for implementing a Kalman filter. However, such a table may require a costly memory for storing values of the table.